Inverse Principle Research Articles

Upper metric mean dimensions with potential on subsets

In this paper, we introduce the notion of upper metric mean dimension with potential on any subset (not necessarily compact or invariant) via Carathéodory–Pesin structures. We discuss several possible versions of upper measure-theoretic mean dimensions with potential and find conditions to make these notions coincide. In particular, we present a corresponding variational principle and an inverse variational principle.

Coupled Generation

Instance generation creates representative examples to interpret a learning model, as in regression and classification. For example, representative sentences of a topic of interest describe the topic specifically for sentence categorization. In such a situation, a large number of unlabeled observations may be available in addition to labeled data, for example, many unclassified text corpora (unlabeled instances) are available with only a few classified sentences (labeled instances). In this article, we introduce a novel generative method, called a coupled generator, producing instances given a specific learning outcome, based on indirect and direct generators. The indirect generator uses the inverse principle to yield the corresponding inverse probability, enabling to generate instances by leveraging an unlabeled data. The direct generator learns the distribution of an instance given its learning outcome. Then, the coupled generator seeks the best one from the indirect and direct generators, which is designed to enjoy the benefits of both and deliver higher generation accuracy. For sentence generation given a topic, we develop an embedding-based regression/classification in conjuncture with an unconditional recurrent neural network for the indirect generator, whereas a conditional recurrent neural network is natural for the corresponding direct generator. Moreover, we derive finite-sample generation error bounds for the indirect and direct generators to reveal the generative aspects of both methods thus explaining the benefits of the coupled generator. Finally, we apply the proposed methods to a real benchmark of abstract classification and demonstrate that the coupled generator composes reasonably good sentences from a dictionary to describe a specific topic of interest. Supplementary materials for this article are available online.

An investigation of network growth principles in the phonological language network.

This article investigated how network growth algorithms-preferential attachment, preferential acquisition, and lure of the associates-relate to the acquisition of words in the phonological language network, where edges are placed between words that are phonologically similar to each other. Through an archival analysis of age-of-acquisition norms from English and Dutch and word learning experiments, we examined how new words were added to the phonological network. Across both approaches, we found converging evidence that an inverse variant of preferential attachment-where new nodes were instead more likely to attach to existing nodes with few connections-influenced the growth of the phonological network. We suggest that the inverse preferential attachment principle reflects the constraints of adding new phonological representations to an existing language network with already many phonologically similar representations, possibly reflecting the pressures associated with the processing costs of retrieving lexical representations that have many phonologically similar competitors. These results contribute toward our understanding of how the phonological language network grows over time and could have implications for the learning outcomes of individuals with language disorders. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Research on extended hypoplastic model and its verification for deposits soil

In order to illustrate the mechanical properties of the coarse-grained deposits soil, a series of large scale triaxial tests of deposits soil from the southwest region of China were carried out. Based on the test data and the basic idea of hypoplasticity, the Wu-Bauer hypoplastic model was extended to describe the mechanical behavior of the deposits soil, so that the constructed equations were induced for developed analysis. The model parameter identification method was proposed for the establishment of extended hypoplastic constitutive model by using improved differential evolution algorithm, which was targeted to find the optimization of the error function between test and theoretical results instructed by the inverse analysis principle. Then, an optimization calculation program was written to achieve the identification of the constitutive model parameters, which showed that the proposed identification method was better than the conventional method of parameter determination. Moreover, the test data and numerical calculation of one-dimensional compression test and triaxial test were compared, which indicated that the extended Wu-Bauer hypoplastic model could reflect the different mechanical properties of the deposits soil under different initial conditions.

Optical soliton perturbation with Kudryashov's equation by semi–inverse variational principle

The semi–inverse variational principle retrieved bright 1–soliton solution to the perturbed Kudryashov's equation. The perturbation terms appear with maximum intensity and additionally higher order dispersion effects are included. The parameter constraints for the solitons to exist are also enumerated.

The response surface method-genetic algorithm for identification of the lumbar intervertebral disc material parameters

Long-term compressive load on the lumbar intervertebral disc (IVD) might lead to lumbar IVD herniation. Exploring the material parameters of normal and degenerative enucleated IVDs is the basis for studying their mechanical behavior. According to the inverse analysis principle of the parameter estimation, an optimization method was proposed to identify the parameters of the porous material of the lumbar IVD based on finite element inverse analysis. The poroelastic finite element models were established in line with the compression creep experiment. The material parameters were combined by Box–Behnken design (BBD), and the response surface (RS) models were constructed using a quadratic polynomial with cross terms and optimized by genetic algorithm (GA). The results showed that the simulation result of the best material parameter combination had a good agreement with the experiment. Compared with the normal lumbar IVD, the elastic modulus and permeability decreased, and Poisson's ratio increased for the enucleated disk, resulting in a significant difference in mechanical properties. The algorithm used in this study can reduce the parameter identification error compared with only the RS method, and decrease the number of finite element simulations compared with only the GA.

Adaptive fuzzy output feedback inverse optimal control for vehicle active suspension systems

In this paper, the adaptive fuzzy inverse optimal output feedback control problem for vehicular active suspension systems (ASSs) is addressed. The considered vehicular active suspension system (ASS) is a quarter-car model with electromagnetic actuators and contains unknown nonlinear characteristics. The fuzzy logic systems (FLSs) are used to approximate unknown nonlinearities, and an auxiliary system model is constructed. Based on auxiliary system model, a fuzzy state observer is designed to estimate immeasurable states. By using adaptive backstepping design technique and inverse optimal principle, an adaptive fuzzy output feedback inverse optimal strategy is proposed. The developed adaptive fuzzy inverse optimal output feedback control method not only guarantees that the attitude of the vehicle is stabilized, but also achieves inverse optimization in relation to the cost functional. Finally, the simulation studies are given in the cases of both bump road and sinusoid road displacement input, and the simulation results show the validity of the proposed control method.

Observer-Based Fuzzy Adaptive Inverse Optimal Output Feedback Control for Uncertain Nonlinear Systems

In this article, an observer-based fuzzy adaptive inverse optimal output feedback control problem is studied for a class of nonlinear systems in strict-feedback form. The considered nonlinear systems contain unknown nonlinear dynamics and their states are not measured directly. Fuzzy logic systems are applied to identify the unknown nonlinear dynamics and an auxiliary nonlinear system is constructed. Based on this auxiliary system, a fuzzy state observer is first designed to estimate the immeasurable states. By using the inverse optimal principle and adaptive backstepping design theory, an observer-based fuzzy adaptive inverse optimal output feedback control scheme is then developed. The proposed inverse optimal control scheme need not assume that the states are measurable. It also guarantees that the closed-loop system is semiglobally uniformly ultimately bounded, and achieves the optimal control objective as well. Finally, two simulation examples are provided to check the validity of the presented control method.

Failure mechanism and fracture aperture characteristics of hard thick main roof based on voussoir beam structure in longwall coal mining

AbstractThe mechanism and fracture aperture of thick hard roof failure were theoretically analyzed from the perspective of elastoplastic mechanics. A uniform load cantilever beam was established by considering the voussoir beam structure and stress condition. According to the stress inverse principle in solving the plane strain problem, the internal stress component analytic solution was deduced. Considering the lateral thrust and shear force and by applying the Mohr‐Coulomb failure criterion, the plastic zone boundary equation was obtained. Further analysis of the equivalent stress, equivalent strain, elastic energy density, distortion energy density, and strain energy density was studied with blocks of four different lengths, combined with the rotation angles after failure, to analyze the fissure aperture between straight and curved fracture traces. The theoretical analysis reveals that the deviatoric effect plays the lead role in rupture initiation and propagation; the cracks will deflect during failure, and the fracture trace presents a curved shape. The variation of fracture aperture exhibits a tendency to increase first, then decrease, and then increase along the fracture trace. The analytical approach presented in this paper provides a theoretical basis for determining the main seepage channel flow in underground mining.

Measurement of Maximum Deviation from Roundness Based on the Inverse Kinematics Principle

Abstract The article deals with a special method of measuring the maximum deviation of objects from roundness based on the inverse kinematics principle. The inverse measurement mechanism is based on the immobility of the measuring probes and the object performing all the motions required to measure a dimension. The advantage of this principle is minimization of the temperature change, while the adverse effect in the measurement system is greatly reduced at the same time. The measurement methodology requires a special software evaluation of the data measured. The aim of the given measurement methodology was to establish the maximum roundness deviation that corresponds to the Least Squares Circle (LSC) method. An experiment with three measuring probes was conducted to verify the methodology.

Highly dispersive optical soliton perturbation with quadratic–cubic refractive index by semi–inverse variational principle

This paper gives highly dispersive perturbed bright optical solitons with quadratic–cubic law of refractive index. The semi–inverse variational principle makes this retrieval possible with Hamiltonian perturbations.

Analytical model for the winding process-induced residual stresses of the multilayered filament wound cylindrical composite parts

The residual stresses due to winding tensions have significant influence on the product quality of the filament wound composite parts. In this paper, an analytical model is proposed to calculate the winding process-induced residual stresses for the multilayered filament wound composite parts with metal linear based on the three-dimensional thick-walled cylinder theory. In the modeling of winding process, the contribution of the current outmost winding tension to the residual stresses of the previously wound composite layers is first calculated and then the total residual stresses is obtained based on the elastic superposition principle. Moreover, the winding tensions are modified for equal residual stress in fibers based on the inverse iteration principle. Compared with the results in other work and obtained by finite element method, it shows that the proposed analytical model is of high accuracy and can be used to calculate the residual stresses due to winding tensions for the multilayered filament wound composite parts. The expected winding tensions for the equal residual fiber stresses can be quickly obtained after several iterations. Moreover, the effects of thickness of metal linear on the winding tensions distributions are further investigated based on the proposed model and the iterative algorithm.

Influence of Stimulus Intensity on Multimodal Integration in the Startle Escape System of Goldfish.

Processing of multimodal information is essential for an organism to respond to environmental events. However, how multimodal integration in neurons translates into behavior is far from clear. Here, we investigate integration of biologically relevant visual and auditory information in the goldfish startle escape system in which paired Mauthner-cells (M-cells) initiate the behavior. Sound pips and visual looms as well as multimodal combinations of these stimuli were tested for their effectiveness of evoking the startle response. Results showed that adding a low intensity sound early during a visual loom (low visual effectiveness) produced a supralinear increase in startle responsiveness as compared to an increase expected from a linear summation of the two unimodal stimuli. In contrast, adding a sound pip late during the loom (high visual effectiveness) increased responsiveness consistent with a linear multimodal integration of the two stimuli. Together the results confirm the Inverse Effectiveness Principle (IEP) of multimodal integration proposed in other species. Given the well-established role of the M-cell as a multimodal integrator, these results suggest that IEP is computed in individual neurons that initiate vital behavioral decisions.

Multimodal Object Classification Models Inspired by Multisensory Integration in the Brain.

Two multimodal classification models aimed at enhancing object classification through the integration of semantically congruent unimodal stimuli are introduced. The feature-integrating model, inspired by multisensory integration in the subcortical superior colliculus, combines unimodal features which are subsequently classified by a multimodal classifier. The decision-integrating model, inspired by integration in primary cortical areas, classifies unimodal stimuli independently using unimodal classifiers and classifies the combined decisions using a multimodal classifier. The multimodal classifier models are implemented using multilayer perceptrons and multivariate statistical classifiers. Experiments involving the classification of noisy and attenuated auditory and visual representations of ten digits are designed to demonstrate the properties of the multimodal classifiers and to compare the performances of multimodal and unimodal classifiers. The experimental results show that the multimodal classification systems exhibit an important aspect of the “inverse effectiveness principle” by yielding significantly higher classification accuracies when compared with those of the unimodal classifiers. Furthermore, the flexibility offered by the generalized models enables the simulations and evaluations of various combinations of multimodal stimuli and classifiers under varying uncertainty conditions.

Fractional order model and Lump solution in dusty plasma

In recent years, the dust plasma research plays an important role in the field of space, industry, and laboratory. In this paper, starting from the control equations of the double temperature dust plasma, we derive the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation to describe the double temperature dust plasma sound waves by using the multi-scale analysis, and reduce it by using the perturbation method. Then by using the semi inverse method and fractional variational principle, the (2+1)-dimensional KP equation is introduced into the time-space fractional KP equation (TFS-KP). The fractional KP equation has potential applications in describing physical phenomena in practical problems. Furthermore, based on the symmetrical analysis method, by which lie discussed the time fractional KP (TF-KP) equation of the conservation law, the dual temperature dust plasma acoustic conserves quantity. Finally, based on the bilinear method, the lump solution of fractional KP equation is obtained. The existence of this solution indicates the rogue waves existing in double temperature dusty plasma. The influence of fractional order on rogue wave is also analyzed.

Riemann zeta factorial function

This paper focuses on extending the theory of Riemann zeta function to Riemann zeta factorial function for infinite series using inverse principle of forward difference operator. This newly introduced series is generated by replacing polynomial by polynomial factorial in Riemann zeta function. Several formulae on higher order Riemann zeta factorial functions have been derived. Suitable examples are inserted to validate the above findings.

High step‐up three level boost converter with inverse characteristic

This paper presents a novel magnetically coupled dual switches three level dc–dc converter with high-voltage boost and reduced power device voltage stress ability. The topology can achieve high-voltage boost ability by using coupled inductor and low MOSFET voltage stress by using three-level idea. However, unlike other high step-up three level converters, its gain is increased by reducing turns ratio. The name inverse is used for representing the inverse proportion principle of the proposed converter. Aiming at existing leakage inductance, introduced diode and capacitor circuit not only absorbs the leakage energy but also further boosts the gain. In addition, the proposed converter only utilises one magnetic core. Operating principles and relevant theoretical analysis of the proposed converter are described. In order to verify the proposed converter's performance, the relevant experiment is performed.

Arak Inequalities for Concentration Functions and the Littlewood--Offord Problem

Let $X,X_1,\ldots,X_n$ be independent identically distributed random variables. In this paper we study the behavior of concentration functions of weighted sums $\sum_{k=1}^{n}a_k X_k$ with respect to the arithmetic structure of coefficients $a_k$ in the context of the Littlewood--Offord problem. Concentration results of this type received renewed interest in connection with distributions of singular values of random matrices. Recently, Tao and Vu proposed an Inverse Principle in the Littlewood-Offord problem. We discuss the relations between the Inverse Principle of Tao and Vu as well as that of Nguyen and Vu and a similar principle formulated for sums of arbitrary independent random variables in the work of Arak from the 1980's.

Comparison of different spatial mathematical models of the extruder screw channel

One of the important problems in the processing of polymeric materials by an extrusion method is the occurrence of local overheating. The aim of this work is to identify these areas and finding ways to reduce their influence on the finished product. The paper discusses the heat and mass transfer processes, which occur in the extruder screw channel. In the work a comparison of the results, obtained by various mathematical models, was made: a flat channel model (full-scale), and the screw channel models with regard to the gap between the screw crest and the inner surface of the body and without it. The investigation of the possibility of using the inverse movement principle in the study of the problems, associated with the cable insulating on the extrusion equipment was made. As a result of research, temperature fields at the outlet of the extruder channel were obtained.

A principle curvatures analysis of the isothermal evolution of nanoporous gold: Quantifying the characteristic length-scales

A study of the isothermal evolution of a nanoporous gold (npg) microstructure after dealloying has been performed. In order to adequately characterize its complex three-dimensional bicontinuous ligament-ring structure, an analysis of the scaled principle curvatures κ1 and κ2 based on representative volumes of meshed 3D reconstructions was applied. Five npg samples, as obtained from an electrolytical dealloying process, with different mean ligament diameters ranging from ca. 25 nm (as-dealloyed) to ca. 420 nm (from annealing at 300° C) were analyzed. The results indicate that ligament surface flattening effects lead to small but distinct morphological changes during the investigated early and mid-stages of coarsening, visible in the scaled κ1- and κ2- marginal distributions. Thus, strictly speaking, self-similar evolution of npg cannot be confirmed, but dependent on the specific application, the evolution might be seen as “sufficiently” self-similar. Moreover, it is shown that the inverse mean principle curvatures from the marginal distributions can be used to identify the mean sizes of the two salient structural features, namely the ligaments and the rings. Both inverse mean principle curvatures scale linearly with the mean ligament diameter. Thus, for the material used in this study, one parameter is sufficient to characterize its microstructure. Finally, it is shown that rings resembling the ones from the real samples can be generated computationally by applying modified torus parameterizations. Surprisingly, a calculation of the curvature distribution of only one ”average” ring is sufficient to approximate the scaled kappa distributions accumulated from the ring distributions of the real samples.